Atomic clock simulation
Project description
stochasticclock
A module calculating the stochastic deviations in timepoints for atomic clocks.
This module is an application of the theory presented in Galleani et al. (2003), doi:10.1088/0026-1394/40/3/305.
The module's current functionality calculates stochastic deviations using the exact iterative solution to the stochastic differential equation in Galleani_exact()
$$\begin{equation*} \mathbf{X}(t_{n+1}) = \begin{pmatrix} 1 & \delta t \\ 0 & 1 \end{pmatrix} \mathbf{X}(t_n) + \begin{pmatrix} \delta t \mu_1 + \frac{1}{2} \delta t^2 \mu_2 \\ \delta t \mu_2 \end{pmatrix} + \mathbf{\Sigma}(t_n) \end{equation*}$$
$$\begin{equation*} \mathbf{\Sigma}(t_n) \sim \mathcal{N} \bigg( \mathbf{0}, \begin{bmatrix} \sigma_1^2 \delta t + \frac{1}{3} \sigma_2^2 \delta t^3 & \frac{1}{2}\sigma_2^2 \delta t^2 \\ \frac{1}{2}\sigma_2^2 \delta t^2 & \sigma_2^2 \delta t \end{bmatrix} \bigg) \end{equation*}$$
Stochastic deviations can be visualised using clock_error()
, and their distributions simulated with deviation_distribution()
.
Please consult the Jupyter notebook for a walkthrough of the package.
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